Simplify the following expression and state the condition under which the simplification is valid. $x = \dfrac{p^2 - 36}{p + 6}$
First factor the polynomial in the numerator. The numerator is in the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as $({a} + {b})({a} - {b})$ $ a = p$ $ b = \sqrt{36} = 6$ So we can rewrite the expression as: $x = \dfrac{({p} + {6})({p} {-6})} {p + 6} $ We can divide the numerator and denominator by $(p + 6)$ on condition that $p \neq -6$ Therefore $x = p - 6; p \neq -6$